Nonlinear control with distributed delay for angular stabilization of a rigid body

Abstract

The problem of angular stabilization of a rigid body with an arbitrary triaxial ellipsoid of inertia is solved. The control strategy is based on the type of PID controller, in which, instead of the classical integral term, a more flexible control option is used, which assumes the presence of a distributed delay (integral term) in the control torque. In addition, instead of the usual linear restoring torque, a non-linear uniform restoring torque is used for the first time. The analytical substantiation of the asymptotic stability of the program motion is based on the use of a special construction of the Lyapunov—Krasovskii functional. A theorem is proved that gives sufficient conditions for the asymptotic stability of the program mode of the body angular motion in the form of constructive inequalities with respect to control parameters. The effectiveness of the constructed control is demonstrated, which simultaneously provides the convergence speed and smoothness of transient process.